NUMERICAL SIMULATION OF AN IN-SITU COMBUSTION MODEL FORMULATED AS MIXED COMPLEMENTARITY PROBLEM

Authors

  • Angel E. Ramírez Gutiérrez IMCA
  • Sandro Mazorche Universidade Federal de Juiz de Fora
  • Grigori Chapiro Universidade Federal de Juiz de Fora

DOI:

https://doi.org/10.26512/ripe.v2i17.21657

Keywords:

In situ combustion. Conservation laws. Mixed complementarity problem.

Abstract

The difficulty of the extraction of medium and heavy oil is its hight viscosity. One form of decreasing it consists in applying the thermal methods as steam injection or in-situ combustion. In the present work one simple model for in-situ combustion is presented. It consists of two nonlinear partial differential equations. As obtaining the analytical solutions for this type of equation is near impossible, it is necessary to make computational simulations. In fact, the solutions for in-situ combustion problem involves shock waves, which increases the difficulty of the numerical simulations. A possible way to avoid this problem is to rewrite the differential equations as one mixed nonlinear complementarity problem. In this work numerical simulations are performed using the finite difference method and a feasible directions algorithm for mixed nonlinear complementarity problem to obtain approximate solutions of the proposed model. The results are compared with ones obtained by using the Newton’s method that was used in other references.

Downloads

Download data is not yet available.

References

Akkutlu, I. Y. and Yortsos, Y. C. (2003). The dynamics of in-situ combustion fronts in porous media. Combustion and Flame, 134(3):229”“247.

Bruining, J., Mailybaev, A., and Marchesin, D. (2009). Filtration combustion in wet porous medium. SIAM Journal on Applied Mathematics, 70(4):1157”“1177.

Chapiro, G., Mailybaev, A. A., de Souza, A. J., Marchesin, D., and Bruining, J. (2012). Asymptotic approximation of long-time solution for low-temperature filtration combustion. Computational geosciences, 16(3):799”“808.

Chapiro, G., Marchesin, D., and Schecter, S. (2014). Combustion waves and riemann solutions in light porous foam. Journal of Hyperbolic Differential Equations, 11(02):295”“328.

Chapiro, G., Mazorche, S., Herskovits, J., and Roche, J. (2010). Solution of the nonlinear parabolic problem using nonlinear complementarity algorithm (fda-ncp). Mec´anica Computacional, 29(20).

Chapiro, G., Ram´Ä±rez G., A. E., Herskovits, J., Mazorche, S. R., and Pereira, W. S. (2016). Numerical solution of a class of moving boundary problems with a nonlinear complementarity approach. Journal of Optimization Theory and Applications, 168(2):534”“550.

Chen, C. and Mangasarian, O. L. (1996). A class of smoothing functions for nonlinear and mixed complementarity problems. Computational Optimization and Applications, 5(2):97”“ 138.

Gharbia, I. B. and Jaffr´e, J. (2014). Gas phase appearance and disappearance as a problem with complementarity constraints. Mathematics and Computers in Simulation, 99:28”“36.

Gupta, R. and Kumar, D. (1981). Variable time step methods for one-dimensional stefan problem with mixed boundary condition. International Journal of Heat and Mass Transfer, 24(2):251”“259.

Gupta, R. S. (2015). Elements of Numerical Analysis. Cambridge University Press.

Herskovits, J. (1998). Feasible direction interior-point technique for nonlinear optimization. Journal of optimization theory and applications, 99(1):121”“146.

Herskovits, J. and Mazorche, S. R. (2009). A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics. Structural and Multidisciplinary Optimization, 37(5):435”“446.

Lauser, A., Hager, C., Helmig, R., and Wohlmuth, B. (2011). A new approach for phase transitions in miscible multi-phase flow in porous media. Advances inWater Resources, 34(8):957”“ 966.

LeVeque, R. J. (1992). Numerical methods for conservation laws, volume 132. Springer.

Mazorche, S. and Herskovits, J. (2005). A new interior point algorithm for nonlinear complementarity problems. In Sixth World Congress on Structural and Multidisciplinary Optimization-CD Proceedings, pages 13”“14.

Morton, K. W. and Mayers, D. F. (2005). Numerical solution of partial differential equations: an introduction. Cambridge university press.

Strikwerda, J. C. (1989). Finite difference schemes and partial differential equations, Wadsworth Publ. Co., Belmont, CA.

Downloads

Published

2017-01-30

How to Cite

Gutiérrez, A. E. R., Mazorche, S., & Chapiro, G. (2017). NUMERICAL SIMULATION OF AN IN-SITU COMBUSTION MODEL FORMULATED AS MIXED COMPLEMENTARITY PROBLEM. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(17), 172–181. https://doi.org/10.26512/ripe.v2i17.21657